Imported video's audio has different play time when watching in vlc
Okay so I finally figured it out!



I thought this would have only mattered if the recorded video was defined as a variable frame rate video, and things were broken even after explicitly converting it to a constant 30fps.  But lo and behold, I changed that setting to AV-Sync and everything works beautifully!

Hope this helps anyone else looking for the answer to this problem.